The link between extreme precipitation and convective ......has a magnitude of 20% K −1 at the 99th percentile and 149% K 1 at the 99.9th percentile. 3. Convective Organization In

GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1002/,

The link between extreme precipitation and

convective organization in a warming climate: Global

radiative convective equilibrium simulations

Angeline G. Pendergrass1,2, Kevin A. Reed3, Brian Medeiros2

Corresponding author: Angeline G. Pendergrass, P.O. Box 3000, Boulder, CO 80307. (ap-

[email protected])

1CIRES, University of Colorado and

Climate and Global Dynamics Laboratory,

National Center for Atmospheric Research,

Boulder, Colorado, USA.

2Climate and Global Dynamics

Laboratory, National Center for

Atmospheric Research, Boulder, Colorado,

USA.

3School of Marine and Atmospheric

Sciences, State University of New York at

Stony Brook, Stony Brook, New York, USA.

D R A F T October 19, 2016, 10:08am D R A F T

X - 2 PENDERGRASS ET AL.: EXTREME PRECIPITATION AND CONVECTIVE ORG.

Key Points.

◦ The rate of extreme precipitation change

with warming can differ substantially from

the rate of moistening.

◦ Convective organization varies with warm-

ing in climate model radiative-convective

equilibrium simulations.

◦ The rate of extreme precipitation change

with warming varies with changing convec-

tive organization.

The rate of increase of extreme precipita-

tion in response to global warming varies dra-

matically across climate model simulations,

particularly over the tropics, for reasons that

have yet to be established. Here, we propose

one potential mechanism: changing organiza-

tion of convection with climate. We analyze

a set of simulations with the Community At-

mosphere Model version 5 (CAM5) with an

idealized global radiative-convective equilib-

rium configuration forced by fixed SSTs vary-

ing in two-degree increments from 285 to 307

K. In these simulations, convective organiza-

tion varies from semi-organized in cold sim-


PENDERGRASS ET AL.: EXTREME PRECIPITATION AND CONVECTIVE ORG. X - 3

ulations, disorganized in warm simulations,

and abruptly becomes highly organized at just

over 300 K. The change in extreme precipi-

tation with warming also varies across these

simulations, including a large increase at the

transition from disorganized to organized con-

vection. We develop an extreme-precipitation-

focused metric for convective organization, and

use this to explore their connection.



1. Introduction

The response of the hydrologic cycle to a changing climate is of utmost importance in

evaluating mitigation and adaptation policies. Although some aspects of the hydrologic

cycle have constraints imposed by the global energy budget, the factors driving others

are not yet established. In particular, the balance between global-mean precipitation and

radiative cooling is well understood, as is the expected increase in tropospheric specific

humidity with surface warming; climate models robustly predict global-mean rainfall to

increase at a lower rate than specific humidity [Mitchell et al., 1987]. In contrast, there is

a large spread in the extreme precipitation response, especially in the tropics [O’Gorman

and Schneider , 2009a; O’Gorman, 2012]. If extreme precipitation events are driven by

moisture convergence and circulation in extreme events changes little with warming, then

extreme precipitation change will increase due to the “thermodynamic” effect of increas-

ing saturation vapor pressure, and associated moist adiabatic lapse rate, with warming

[e.g., O’Gorman, 2015]. Much of the change in the distribution of precipitation can be

captured by shifting it to heavier rain rates and increasing the frequency of precipita-

tion evenly at all rain rates [Pendergrass and Hartmann, 2014a]. These changes in the

distribution of precipitation are connected to changes in warming, moistening, and the

distribution of vertical velocity [Pendergrass and Gerber , 2016]. But the high rates of

extreme precipitation increase in some climate models are not captured by movements of

the distribution of precipitation; Pendergrass and Hartmann [2014a] call this deviation

the “extreme mode.” If the circulation associated with extreme events were to dramati-

cally change, the rate of change of extreme precipitation with warming would change as



well. Thus, changes in circulation could be one explanation for the large range in the rate

of extreme precipitation change with warming in climate model simulations.

Extreme precipitation is often associated with organized convection, like tropical cy-

clones and mesoscale convective systems. Although organized convection has long been

recognized as important, recent work has explored convection that can self-organize, both

in observations and models. In numerical modeling studies of convection in idealized

environments, convection forms randomly as the simulation begins, but aggregates into

clusters as it evolves [Bretherton et al., 2005; Muller and Held , 2012; Wing and Emanuel ,

2014]. Depending on characteristics of the simulation (e.g., domain size, grid size, model

formulation), the self-aggregated state represents a stable steady-state of the system, and

eventually a single convective cluster forms and the rest of the model domain has a very

dry, subsiding troposphere. Similar aggregation has recently been described in global cli-

mate models run in idealized configurations [Popke et al., 2013; Reed et al., 2015; Coppin

and Bony , 2015]. Popke et al. [2013] showed that the mean climate of their idealized

configuration closely resembles the tropical climate of comprehensive simulations with

its parent model configuration. In these simulations, the degree of aggregation that oc-

curs depends on the surface temperature [Held et al., 2007; Wing and Emanuel , 2014;

Bony et al., 2016]. An important implication of this dependence is that the nature of

organized convection may change with climate, altering the distribution of precipitation,

including extreme precipitation [Tan et al., 2015]. Two studies have examined changes in

extreme precipitation in the context of organized convection [Muller , 2013; Singleton and



Toumi , 2013], but none have examined the effect of changing organization on extreme

precipitation.

In this paper, we explore the relationship between extreme precipitation and convective

aggregation in a set of climate model simulations with a range of surface temperatures.

Using an idealized climate model configuration, we test the hypothesis that changes in

organization influence extreme precipitation. Our intentions in this study are two-fold: (1)

to illustrate a situation in which circulation, rather than moisture, drives a large increase

in extreme precipitation, and (2) to develop metrics that quantify convective organization

and relate it to extreme precipitation.

2. Model simulations

Twelve global radiative-convective equilibrium (RCE) simulations are run with CAM5,

the atmospheric component of the Community Earth System Model (CESM). Each simu-

lation has a uniform, fixed sea-surface temperature (SST) ranging from 285 to 307 K, runs

for three years, and otherwise follows the methodology of Reed et al. [2015]. These simu-

lations, along with global-RCE simulations from other climate models, have been used to

explore the impact of surface temperature on convective anvil clouds [Bony et al., 2016];

global RCE in CAM5 has also been used for convective process studies [Reed and Chavas ,

2015; Reed and Medeiros , 2016]. The model uses the spectral element dynamical core on

a cubed-sphere grid to solve the equations of motion [Taylor and Fournier , 2010; Dennis

et al., 2012]. Mean grid spacing is 111 km, which is typical for global climate simulations.

The subgrid-scale physics are parameterized with schemes for moist turbulence, shallow

convection, deep convection, cloud microphysics and macrophysics, radiative transfer, and



other processes; these are described in Neale et al. [2012]. The simplifications of the RCE

configuration are: an aquaplanet with globally-uniform prescribed SST, spatially uniform

and diurnally varying insolation with mean 340 W m−2 and equatorial solar zenith angle

[following Popke et al., 2013], and no planetary rotation (no Coriolis force). Greenhouse

gas forcing is held fixed, with carbon dioxide at 348 ppm. Other aspects of the simulations

follow Reed et al. [2015].

Figure 1 shows the mean precipitation from a randomly chosen month for each simu-

lation. The number of precipitating regions and their spatial distribution changes across

the simulations. Throughout this work, we will describe the simulations according to

their prescribed SST and degree of organization: cold simulations are slightly organized,

warm simulations are disorganized, and hot simulations are highly organized. As we will

see in section 3.2, organization in the cold simulation is driven largely by long-lived pre-

cipitating events (Fig. 1 shows monthly rather than daily mean precipitation because

the organization in the cold simulations is not visible in daily fields; the highly-organized

systems in the hot simulations are nearly stationary, so they are evident in both daily and

monthly precipitation). In the three cold simulations, there are multiple events which

are dispersed, with patchy dry regions in between. The six warm simulations have more

precipitating regions than the cold simulations, but each is smaller and weaker, with fewer

dry regions. In each of the three hot simulations, precipitation is focused in one primary

region (though there is more than one local maximum in two of the examples). The dry

regions cover more of the remaining area in hot than in warm simulations.



Mean precipitation increases with warming in comprehensive climate model simulations

[e.g., Held and Soden 2006], so we expect to see total rainfall increase with SST in our

simulations. Figure 2a shows the globally-averaged precipitation calculated over each 3-

year simulation, excluding the first six months for spinup. All simulations except 307 K

reach a stable state in less than 6 months and maintain that state for the duration of the

simulation, in contrast to results reported by Coppin and Bony [2015]. Mean precipitation

increases from each simulation to the next, except from 289 to 291 K (the precipitation

change from each simulation to the next relative to the prescribed 2-K SST change is

shown in Fig. 2b). For reference, Fig. 2c shows the global-mean specific humidity from

the lowest model level (referred to here as near-surface) in each simulation, with saturation

specific humidity at the prescribed SST for reference.

Extreme precipitation is expected to increase more than mean precipitation with warm-

ing [e.g., Trenberth, 1999]. We quantify the extreme precipitation as the average precipita-

tion rate from grid points with at least the 99th percentile of daily rainfall accumulation.

This calculation entails, for each simulation, first forming the frequency distribution of

daily accumulated precipitation following Pendergrass and Hartmann [2014b], excluding

the first six months as spinup (as we did for mean precipitation). Then, we globally aver-

age this frequency distribution and determine its 99th percentile, including both wet and

dry days [Schär et al., 2016]. Finally, we find all grid-point-days with precipitation over

the 99th percentile and area-average their precipitation rates. Figure 2d shows that ex-

treme precipitation is largest in the three hot simulations, lowest in the warm simulations,

and modestly large in the cold simulations.



Figure 2e shows the percentage change in extreme precipitation from each simulation

to the next relative to the change in prescribed SST. Instead of increasing consistently by

the same amount as the moisture holding capacity or average moisture, which would each

be around 7 %K−1 in cold simulations and decrease slightly in warmer simulations, the

extreme precipitation behaves quite differently. Between cold, semi-organized simulations

(


ining global warming simulations because we expect mean OLR to change with warming.

To overcome these challenges and facilitate comparison with precipitation, we develop a

precipitation-based metric for convective organization. Our metric is focused on events,

rather than whole domains, and builds on Tobin et al. [2012]. Instead of an OLR-based

threshold, we use a precipitation intensity threshold: grid cells with precipitation rates of

at least the 99th percentile.

3.1. Event identification and tracking

Our precipitation-centric event identification and tracking algorithm works as follows.

First, we calculate the 99th percentile of precipitation as described in Section 2. Then,

we identify regions of contiguous grid cells with >99th-percentile precipitation for each

day of the simulation. Next, we track the contiguous regions from one day to the next.

Regions are considered to be contiguous if there is an overlap of at least 25% of the area

of the smaller of the regions. Most previous work uses 50% overlap and 6-hourly data.

We use daily data because that is the frequency at which some fields were saved; we chose

the 50% overlap threshold through testing on organized simulations. We accommodate

merging and splitting by requiring that each event constitutes only one contiguous region

per day; in cases of conflict the event with the largest overlapping area continues, and in

a tie, the longer-lived event is chosen. Tracking is done on the native cubed-sphere grid,

which has the advantage that all grid cells have similar area and also allows uninterrupted

movement of events across the poles.



3.2. Convective Aggregation Index

Using the event identification and tracking algorithm, we quantify convective organiza-

tion in each simulation. We define a Convective Aggregation Index (CAI),

CAI ≡ND

T, (1)

where N is the average number of events, D is the average distance between events

(arithmetic mean cluster distance D1, as defined in Tobin et al. [2012]), and T is the

average event duration, weighted by event area. Smaller CAI implies more organization.

CAI extends the metric developed in Tobin et al. [2012] by incorporating event duration,

which is necessary to capture the organization in the cold simulations. The high degree

of organization in the hot simulations is robust to different metrics.

Figure 2f-i show N , D, T , and the CAI for each simulation. Convective organization is

a minimum at moderate, tropical-like temperatures (Fig. 2i). CAI captures the essential

organizing behavior apparent in Fig. 1: cold simulations that are moderately organized,

decreasing organization through the warm simulations, and an abrupt transition to high

organization in the three hottest simulations. N is largest in the cold simulations, de-

creases abruptly from 293 to 295 K, and decreases again from 301 to 303 K. D quantifies

the spacing between events: organization increases when events clustered in space, leaving

a larger dry region. When events are clustered, the convection is more organized and D is

small. D is relatively steady until 303 K, when it decreases abruptly. T is longest in 303

and 305 K simulations, moderate in the cold and the hottest simulations, and shortest in

the warm simulations.



An alternative quantification of organization is the fraction of total rain falling in ex-

treme events (>99th-percentile precipitation) as a function of the event size (Fig. 2k).

Extreme-event precipitation is binned by the logarithm of event area into 100 bins with

exponentially increasing width, with edges distributed evenly in logarithmic space from

log 104 to log 107 m2, and then normalized by the simulation’s total precipitation. Each

resulting distribution of precipitation fraction by event area sums to the fraction of total

precipitation falling in all extreme events (Fig. 2j). The fraction of precipitation falling in

extreme events is higher for more organized simulations. In cold and warm simulations,

the distribution of precipitation by extreme event size is centered at around 2× 105 km2.

In the hot simulations, the distribution is bimodal: some precipitation falls in events with

the same size as cooler simulations, but more falls in larger events (∼ 3× 106 km2). The

hottest simulation is an exception, with the most precipitation from events of moderate

size. Despite that cold and warm simulations have peak precipitation fraction at similar

event size, a larger fraction of rain falls in extreme events in the cold simulations compared

to the warm ones because event duration is longer in the cold simulations (Fig. 2h).

The contributions of large-scale and convective precipitation to the rain amount distri-

bution provide another indication that the cold and hot simulations are more organized

than the warm ones (Fig. S1, following Pendergrass and Hartmann 2014a). In the hot

simulations, the rain amount distribution has an extension to very heavy rain rates which

includes a substantial contribution from from large-scale precipitation, indicating that the

circulations involved are resolved. The cold simulations also have substantial contributions

from large-scale precipitation centered heavy rain rates relative to their distributions. In



contrast, in the warm simulations, the most large-scale precipitation occurs at rain rates

that also have substantial convective precipitation.

4. Circulation changes with convective organization

Figure 3 shows 850 hPa vertical velocity, near-surface specific humidity, and profiles of

temperature and vertical velocity area-averaged over events with >99th-percentile pre-

cipitation for each simulation. The 850 hPa vertical velocity is strongest in the coldest

and hottest simulations, and weakest for the warm simulations. The weakening from cold

to warm simulations is gradual, while the strengthening from warm to hot simulations is

abrupt between 301 and 303 K. The specific humidity, on the other hand, increases steadily

with warming. Temperature increases throughout the troposphere with increasing SST,

with additional amplified of warming aloft in the hot simulations.

The vertical velocity profile averaged over all extreme events in each simulation is shown

in Fig. 3d. The maximum vertical velocity achieved occurs between 500 and 600 hPa in

the cold simulations. These simulations have extreme events with convection reaching

the tropopause (which rises with SST). The warm simulations have the weakest vertical

velocities throughout the column, with some showing a local minimum around 700 hPa,

indicating that extreme events are shallow. The hot simulations have vertical velocity

maxima near 800 hPa, shallower than the cold simulations, but with strong ascent over a

larger fraction of the troposphere.

5. Mechanisms of extreme precipitation change

To isolate the dynamic effects of changing vertical velocity from the thermodynamic ef-

fects of changing temperature, we apply the extreme precipitation scaling from O’Gorman



and Schneider [2009a] to the CAM5 global-RCE simulations, and make a set of sensitivity

calculations (Fig. 4). The extreme precipitation scaling is the integral of condensed water

due to vertical advection of moisture along a moist adiabat,

Pe ≈

∫ ps

pt

dp

gωdqsdp

∣

∣

∣

∣

θ∗,Te

, (2)

where Pe is the >99th-percentile precipitation, pt is the tropopause pressure (the highest

level with a lapse rate of 2 K km−1), ps is the surface pressure, g is the gravitational

constant, ω is the vertical velocity profile, and dqs/dp is the vertical derivative of saturation

vapor pressure. The extremes scaling is calculated on profiles of temperature Te (Fig. 3c)

and vertical velocity (Fig. 3d) area-averaged over all >99th-percentile events in each

simulation, otherwise following O’Gorman and Schneider [2009a]. We did not use grid-

point or event-averaged profiles because our tests indicate that these result in less accurate

fits to the change in extreme precipitation across the simulations. We speculate that the

difference arises because the scaling does not account for local downdrafts associated with

horizontal advection, which averaging removes.

In addition to applying the extremes scaling to the profiles from each simulation

(Fig. 4a), we perform three sensitivity calculations which isolate the effects of vary-

ing the anomalous temperature profile, vertical velocity, and temperature. We define the

anomalous temperature profile as the temperature at each level in the troposphere minus

SST. To isolate the effect of the anomalous temperature profile, we fix the vertical velocity

profile at its value in the 299 K simulation, set the surface temperature to 299 K, and

allow the anomalous temperature profile to vary. Results are not sensitive to the choice

of 299 K as the base simulation. To isolate the effect of vertical velocity, we allow it to



vary while holding SST and temperature profile fixed at values from the 299 K simulation

(Fig. 4c). To isolate the effect of temperature, we allow only SST to vary, while hold-

ing vertical velocity and anomalous temperature profiles fixed at values from the 299 K

simulation (Fig. 4d).

The extremes scaling accurately captures the change in extreme precipitation in most

cases (Fig. 4a; c.f. Fig. 2e). It captures the decrease in extreme precipitation with warm-

ing in the cold simulations, the modest increase with warming in the warm simulations,

the jump to much higher extreme precipitation rates from the 301 to 303 K simulations,

and the return to more modest but erratic changes between hot simulations.

Varying only anomalous temperature profile recovers some aspects of the extreme pre-

cipitation change, but not others (Fig. 4b). Among the cold simulations, the extreme

precipitation change is muted, decreasing in one case. There is a local maximum at the

transition from cold to warm, and another at the transition from warm to hot. But the

transition from warm to hot has an increase of 6.7% K−1, far less than the 73% K−1 in

the simulations.

Varying vertical velocity captures important features of the extreme precipitation

change, particularly the large increase from warm to hot simulations (60 % K−1). Further-

more, because we calculate the change in extreme precipitation from one simulation to the

next, the increases are cumulative (e.g. Fig. 2e). Thus, the variation in vertical velocity

alone recovers the transition of extreme precipitation magnitude to much larger values,

which is sustained across the hot simulations. The extreme precipitation decrease between

cold simulations and the variation between hot simulations are also captured, though the



increase in extreme precipitation between warm simulations is underestimated in this

sensitivity calculation.

The effect of increasing surface temperature (Fig. 4d) is to increase extreme precipi-

tation by 6.6% K−1 from one simulation to the next at cold temperatures, with steadily

less increase as SST increases until the 4.0% K−1 between the two hottest simulations.

The effect of increasing temperature is important, but it is not responsible for the rich

behavior of extreme precipitation change with warming that we see in our simulations.

The sum of the three sensitivity calculations closely recovers the scaling of all three

variations together (i.e. Figs. 4b-d sum to Fig. 4a). These sensitivity calculations show

that while extreme precipitation change varies due to changing circulation as well as

temperature, the large increase at the transition from disorganized to organized states

only occurs in response to changing circulation. Within any regime, the variation in

extreme precipitation scaling is small, but between regimes the difference can be large.

6. Discussion and Conclusion

We have examined a set of idealized CAM5 simulations in the global-RCE configura-

tion forced by fixed SSTs varying from 285 to 307 K. In this set of simulations, convective

organization varies from moderate in the coldest simulations, to disorganized in warm

simulations, to highly organized in hot simulations. We have shown that while mois-

ture and global-mean precipitation increase with warming across most of the simulations,

extreme precipitation does not steadily increase with warming; instead, it varies dramat-

ically. Quantifying extreme precipitation by events with at least 99th-percentile daily

precipitation, it can increase by over 70 %K−1 or decrease by more than 10%K−1. Using



a scaling for extreme precipitation based on condensation due to vertical advection along

moist adiabats, we show that the variation in extreme precipitation change across the

simulations can be explained largely by the variation in circulation, with temperature

change playing an important but secondary role.

Due to the nature of the experimental setup, some important cautions regarding our

results deserve to be stated explicitly. First, we do not expect the temperature thresh-

olds here to generalize to Earth or even other models, because the temperatures at which

convective organization changes states are known to vary in different models according

to factors including but not limited to resolution, dynamical core, and parameterization

schemes. Furthermore, our configuration does not include land, the effects of rotation,

or the spatial pattern of insolation. For these reasons, it is important to evaluate the

relevant relationships and their mechanisms in more comprehensive climate model simu-

lations, convection-permitting simulations, and observations; we cannot assume that these

same behaviors are relevant for Earth on the basis of this analysis. That said, Popke et al.

[2013] indicate that global-RCE simulations could be relevant for understanding compre-

hensive climate models. We would expect our results to be most relevant to the equatorial

region, where tropical cyclones and baroclinic eddies play a minor role driving atmospheric

circulation.

Nonetheless, in this study, our goals were to illustrate a situation in which changes in

extreme precipitation with warming vary dramatically due to changes in circulation, and

to develop metrics quantifying convective organization and its relationship to extreme

precipitation. We have presented one potential mechanism for the large increases in



extreme precipitation with warming in some climate models (the “extreme mode” from

Pendergrass and Hartmann 2014a): changing convective organization. It remains to be

seen whether this mechanism plays a role in comprehensive climate model simulations or

observations, but the tools and understanding developed here enable these investigations.

This study demonstrates that one answer to the WCRP grand challenge question What

role does convective aggregation play in climate? [Bony et al., 2015] is that it might be

important for understanding changes in extremes.

Acknowledgments. We thank two anonymous reviewers for their insightful sugges-

tions which improved the manuscript and Robert Wills for helpful discussion. The CAM5

output presented in this study is available on NCAR’s Yellowstone computing platform.

Matlab code to calculate rainfall distributions and identify and track regions can be found

at github.com/apendergrass. Derived data shown in Figs. 2-4 is included in the Supple-

mentary Information. AGP was supported by the CIRES Visiting Fellowship at the

University of Colorado and the ASP Postdoctoral Research Fellowship at NCAR. BM

and AGP were supported by the Regional and Global Climate Modeling Program of

the U.S. Department of Energy’s Office of Science, Cooperative Agreement DE-FC02-

97ER62402. NCAR is sponsored by the National Science Foundation. We acknowledge

high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided

by NCAR’s Computational and Information Systems Laboratory, also sponsored by the

National Science Foundation.



References

Bony, S., B. Stevens, D. M. Frierson, C. Jakob, M. Kageyama, R. Pincus, T. G. Shepherd,

S. C. Sherwood, A. P. Siebesma, A. H. Sobel, and M. Watanabe (2015). Clouds, circu-

lation and climate sensitivity. Nat. Geosci., 8 (4), 261–268, doi:10.1038/NGEO2398.

Bony, S., B. Stevens, D. Coppin, T. Becker, K. A. Reed, A. Voigt, and B. Medeiros

(2016), Thermodynamic control of anvil-cloud amount, Proc. Natl. Acad. Sci., 119 (32),

8927–8932, doi:10.1073/pnas.1601472113.

Bretherton, C. S., P. N. Blossey, and M. Khairoutdinov (2005), An Energy-Balance Anal-

ysis of Deep Convective Self-Aggregation above Uniform SST., J. Atmos. Sci., 62, 4273–

4292, doi:10.1175/JAS3614.1.

Coppin, D., and S. Bony (2015), Physical mechanisms controlling the initiation of convec-

tive self-aggregation in a general circulation model, J. Adv. Model. Earth Syst., 7 (4),

2060–2078, doi:10.1002/2015MS000571.

Dennis, J., J. Edwards, K. J. Evans, O. N. Guba, P. H. Lauritzen, A. A. Mirin, A. St-

Cyr, M. A. Taylor, and P. H. Worley (2012), CAM-SE: A scalable spectral element

dynamical core for the Community Atmosphere Model, Int. J. High Perf. Comput.

Appl., 26, 74–89, doi:10.1177/1094342011428142.

Held, I. M., and B. J. Soden (2006), Robust responses of the hydrological cycle to global

warming, J. Clim., 19 (21), 5686–5699, doi:10.1175/JCLI3990.1.

Held, I. M., M. Zhao, and B. Wyman (2007), Dynamic Radiative Convective Equilibria

Using GCM Column Physics, J. Atmos. Sci., 64, 228, doi:10.1175/JAS3825.11.



Mapes, B. E., and R. A. Houze (1993), Cloud clusters and superclusters over the oceanic

warm pool, Mon. Weather Rev., 121 (5), 1398–1416.

Mitchell, J. F., Wilson, C. A., and Cunnington, W. M. (1987). On CO2 climate sensitivity

and model dependence of results. Q. J. R. Meteorol. Soc., 113 (475), 293–322, doi:

10.1002/qj.49711347517.

Muller, C. (2013), Impact of convective organization on the response of tropical precipita-

tion extremes to warming, J. Clim., 26 (14), 5028–5043, doi:10.1175/JCLI-D-12-00655.1.

Muller, C. J., and I. M. Held (2012), Detailed Investigation of the Self-Aggregation

of Convection in Cloud-Resolving Simulations, J. Atmos. Sci., 69, 2551–2565, doi:

10.1175/JAS-D-11-0257.1.

Neale, R. B., C. C. Chen, A. Gettelman, P. H. Lauritzen, S. Park, D. L. Williamson, A. J.

Conley, R. Garcia, D. Kinnison, J. F. Lamarque, D. Marsh, M. Mills, A. K. Smith,

S. Tilmes, F. Vitt, P. Cameron-Smith, W. D. Collins, M. J. Iacono, R. C. Easter,

S. J. Ghan, X. Liu, P. J. Rasch, and M. A. Taylor (2012), Description of the NCAR

Community Atmosphere Model (CAM 5.0), NCAR Tech. Note NCAR/TN-486+STR,

National Center for Atmospheric Research, Boulder, Colorado, 282 pp.

O’Gorman, P. A. (2012), Sensitivity of tropical precipitation extremes to climate change,

Nat. Geosci., 5 (10), 697–700, doi:10.1038/NGEO1568.

O’Gorman, P. A., and T. Schneider (2009a), The physical basis for increases in precipi-

tation extremes in simulations of 21st-century climate change, Proc. Natl. Acad. Sci.,

106 (35), 14,773–14,777, doi:10.1073/pnas.0907610106.



O’Gorman, P. A. (2015), Precipitation extremes under climate change, Current Climate

Change Reports, 1 (2), 49–59, doi:10.1007/s40641-015-0009-3.

Pendergrass, A. G., and D. L. Hartmann (2014a), Changes in the distribution of rain

frequency and intensity in response to global warming, J. Clim., 27 (22), 8372–8383,

doi:10.1175/JCLI-D-14-00183.1.

Pendergrass, A. G., and D. L. Hartmann (2014b), Two modes of change of the distribution

of rain, J. Clim., 27 (22), 8357–8371, doi:10.1175/JCLI-D-14-00182.1.

Pendergrass, A. G., and E. P. Gerber (2016), The rain is askew: Two idealized models

relating vertical velocity and precipitation distributions in a warming world, J. Clim.,

doi:10.1175/JCLI-D-16-0097.1.

Popke, D., B. Stevens, and A. Voigt (2013), Climate and climate change in a radiative-

convective equilibrium version of ECHAM6, J. Adv. Model. Earth Syst., 5, 1–14, doi:

10.1029/2012MS000191.

Reed, K. A., and D. R. Chavas (2015), Uniformly rotating global radiative-convective

equilibrium in the community atmosphere model, version 5, J. Adv. Model. Earth Syst.,

7 (4), 1938–1955, doi:10.1002/2015MS000519.

Reed, K. A., and B. Medeiros (2016), A reduced complexity framework to bridge the

gap between agcms and cloud-resolving models, Geophys. Res. Lett., 43 (2), 860–866,

doi:10.1002/2015GL066713, 2015GL066713.

Reed, K. A., B. Medeiros, J. T. Bacmeister, and P. H. Lauritzen (2015), Global radiative–

convective equilibrium in the Community Atmosphere Model, Version 5, J. Atmos. Sci.,

72 (5), 2183–2197, doi:10.1175/JAS-D-14-0268.1.



Schär, C., N. Ban, E. M. Fischer, J. Rajczak, J. Schmidli, C. Frei, F. Giorgi, T. R. Karl,

E. J. Kendon, A. M. K. Tank, et al. (2016), Percentile indices for assessing changes in

heavy precipitation events, Clim. Change, pp. 1–16, doi:10.1007/s10584-016-1669-2.

Singleton, A., and R. Toumi (2013), Super-Clausius–Clapeyron scaling of rainfall in a

model squall line, Q. J. R. Meteorol. Soc., 139 (671), 334–339, doi:10.1002/qj.1919.

Tan, J., C. Jakob, W. B. Rossow, and G. Tselioudis (2015), Increases in tropical rainfall

driven by changes in frequency of organized deep convection, Nature, 519 (7544), 451–

454, doi:10.1038/nature14339.

Taylor, M. A., and A. Fournier (2010), A compatible and conservative spectral el-

ement method on unstructured grids, J. Comput. Phys., 229, 5879–5895, doi:

10.1016/j.jcp.2010.04.008.

Tobin, I., S. Bony, and R. Roca (2012), Observational evidence for relationships between

the degree of aggregation of deep convection, water vapor, surface fluxes, and radiation,

J. Clim., 25 (20), 6885–6904, doi:10.1175/JCLI-D-11-00258.1.

Trenberth, K. E. (1999), Conceptual framework for changes of extremes of the hydrological

cycle with climate change, Wea. Clim. Extremes, pp. 327–339, doi:10.1007/978-94-015-

9265-9 18.

Wing, A. A., and K. A. Emanuel (2014), Physical mechanisms controlling self-aggregation

of convection in idealized numerical modeling simulations, J. Adv. Model. Earth Syst.,

6 (1), 59–74, doi:10.1002/2013MS000269.



Figure 1. Monthly mean precipitation from a randomly chosen month for each simulation,

with specified SST at top-left.



0

5

Mean precipitation

mm

/d

(a)

−505

1015

Change in mean precip.

%/K

(b)

0

20

Mean near−surface specific humidity

g/k

g

(c)

0

50

100>99% precipitation

mm

/d

(d)

285 291 295 301 307

020406080

Change in >99% precip.

%/K

(e)

0

50

100N: Number of events

Eve

nts

(f)

0

5

10

15D: Cluster distance

10

6 m

(g)

0

5

10T: Event duration

Days

(h)

0

0.2

0.4CAI: Convective Aggregation Index

10

9 E

vents

*m/d

ay

(i)

285 291 295 301 3070

10

20Mean precip from >99% events

%

(j)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

104 105 106 107

Area (km2)

Pre

cipita

tion fra

ctio

n (

%)

(k)

285

287

289

291

293

295

297

299

301

303

305

307

Figure 2. (a) Global-mean precipitation, (b) change in mean precipitation, (c) global-mean

near-surface specific humidity and saturation specific humidity at each simulation’s specified SST

(line), (d) extreme precipitation (the average rain rate of events over the 99th percentile), and

(e) the change in extreme precipitation between simulations with 2-K SST increments in global

RCE CAM5 simulations. (f) Number of regions N , (g) distance between events (cluster distance

D), (h) event duration T , and (i) Convective Aggregation Index (Eq. 1). (j) Fraction of total

precipitation from events with >99th-percentile rain rate. (k) Fraction of rain contributed by

events as a function of event area (see text for description).



−0.2

0Pressure vertical velocity at 850 hPa

Pa/s

(a)

285 291 295 301 3070

10

20

30Near−surface specific humidity

g/k

g

(b)

200 225 250 275 300

200

400

600

800

1000

Temperature (K)

Pre

ssure

(hP

a)

(c)

−0.6 −0.3 0Pressure vertical velocity (Pa/s)

(d)

285287289291293295297299301303305307

Figure 3. (a) Pressure vertical velocity at 850 hPa, (b) near-surface specific humidity (from

the lowest model level), (c) temperature and (d) vertical velocity profiles averaged over all events

with >99th-percentile daily precipitation.

−20

0

20

40

60

80Extremes scaling

%/K

(a)

285 291 295 301 307

0

10

20Effect of anomalous temperature profile

%/K

(b)

−20

0

20

40

60

80Effect of vertical velocity

%/K

(c)

285 291 295 301 307

0

10

20Effect of temperature

%/K

(d)

Figure 4. (a) Extreme precipitation scaling based on area-averaged profiles of ω and tem-

perature from events with >99th-percentile precipitation. (b) Extremes scaling varying only the

anomalous temperature profile. (c) Extremes scaling varying only the vertical velocity profile.

(d) Extremes scaling varying only the SST. See text for details.


GEOPHYSICAL RESEARCH LETTERS

Supporting Information for “The link between

extreme precipitation and convective organization in

a warming climate: Global radiative-convective

equilibrium simulations”

Angeline G. Pendergrass1,2, Kevin A. Reed3, Brian Medeiros2

Contents of this file

1CIRES, University of Colorado and

Climate and Global Dynamics Laboratory,

National Center for Atmospheric Research,

Boulder, Colorado, USA.

2Climate and Global Dynamics

Laboratory, National Center for

Atmospheric Research, Boulder, Colorado,

USA.

3School of Marine and Atmospheric

Sciences, State University of New York at

Stony Brook, Stony Brook, New York, USA.

D R A F T November 1, 2016, 2:44pm D R A F T

X - 2 PENDERGRASS ET AL.: EXTREME PRECIPITATION AND CONVECTIVE ORGANIZATION

1. Figure S1

2. Tables S1 to S4

Additional Supporting Information

1. Captions for Datasets S1 to S3

Introduction This supporting information provides an addition supporting figure, and

includes the numerical values from Figs. 2-4 of the main text. Tables S1 and S2 show the

data from Fig. 2a-j, Table S3 shows the data from Fig. 3a,b, and Table S4 shows the data

from Fig. 4. Numerical values from Fig. 2k and Figs. 3c,d are included as additional

Data Sets.


PENDERGRASS ET AL.: EXTREME PRECIPITATION AND CONVECTIVE ORGANIZATION X - 3

Data Set S1. The fraction of total precipitation as a function of event area (values

shown in Fig. 2k).

Data Set S2. Temperature profile in each simulation (values from Fig. 3c).

Data Set S3. Vertical velocity profile in each simulation (values from Fig. 3d).



0

2

4

6285 K

0

2

4

6287 K

0

2

4

6289 K

0

2

4

6291 K

0

2

4

6293 K

0

2

4

6295 K

0

2

4

6297 K

0

2

4

6299 K

0

2

4

6301 K

0.1 1 10 1000

2

4

6303 K

0.1 1 10 1000

2

4

6305 K

0.1 1 10 1000

2

4

6307 K

ConvectiveLarge−scale

Rain rate (mm/d)

Rain

am

ount (%

)

Figure S1. The rain amount distribution for each CAM5 global RCE simulation, the contri-

bution from large-scale precipitation (red), and convective precipitation (gray).


PENDERGRASS ET AL.: EXTREME PRECIPITATION AND CONVECTIVE ORGANIZATION X - 5

Table S1. The change from one simulation to the next of mean precipitation and extreme

precipitation (events over the 99th percentile threshold of daily precipitation, Fig. 2b,e).

SST Mean precipitation change >99% precipitation change(K) (% K−1) (% K−1)

287-285 3.0 -3.1289-287 1.4 -11291-289 -1.3 -7.8293-291 2.1 -2.3295-293 3.1 2.1297-295 4.0 5.6299-297 3.4 5.3301-299 3.3 7.0303-301 9.1 73305-303 2.8 5.4307-305 4.5 17

Table S2. Mean precipitation, moisture, extreme precipitation, components of the CAI, and

fraction of total precipitation contributed by extremes for each simulation (Fig. 2a,c,d,f-i).

SST P q qsat >99% P N D T CAI f>99%P(K) (mm d−1) (g/kg) (g/kg) (mm d−1) (Events) (106 m) (109 events m d−1) (Events) (%)285 2.4 4.1 8.6 26 60 10 5.3 0.11 12287 2.6 4.7 9.7 25 71 10.0 5.4 0.13 11289 2.7 5.5 11 19 73 9.8 6.4 0.11 8.4291 2.6 6.0 13 16 90 9.9 5.5 0.16 7.6293 2.7 6.8 14 16 83 9.9 4.4 0.19 6.9295 2.9 8.7 16 16 56 9.7 2.7 0.20 6.8297 3.1 10.0 18 18 68 9.6 2.8 0.23 7.3299 3.3 11 20 20 79 9.7 2.7 0.29 7.4301 3.5 13 23 23 71 9.8 2.7 0.26 7.7303 4.2 16 25 56 25 7.0 9.5 0.018 14305 4.4 18 28 62 25 6.5 8.3 0.020 15307 4.8 20 32 84 27 7.9 5.4 0.039 18



Table S3. Vertical velocity at 850 hPa and specific humidity from the lowest atmosphere level

for each simulation (Fig. 3 a,b).

SST ω850 q(K) (Pa s−1) (g/kg)285 -0.27 5.3287 -0.22 5.9289 -0.16 6.5291 -0.14 7.0293 -0.13 7.9295 -0.12 9.8297 -0.13 11299 -0.13 13301 -0.12 14303 -0.24 17305 -0.23 19307 -0.28 22

Table S4. Extremes scaling and the effect of anomalous temperature profiles, vertical velocity,

and temperature (Fig. 4).

SST Extremes Scaling Anomalous temp. profile Vertical velocity Temperature(K) (% K−1) (% K−1) (% K−1) (% K−1)

287-285 6.6 0.51 -7.6 6.6289-287 6.3 0.50 -13 6.3291-289 6.0 -1.2 -11 6.0293-291 5.7 0.60 -10.0 5.7295-293 5.4 4.1 -13 5.4297-295 5.1 1.7 2.2 5.1299-297 4.9 1.2 -2.0 4.9301-299 4.6 1.5 -1.9 4.6303-301 4.4 6.7 60 4.4305-303 4.2 1.7 -0.067 4.2307-305 4.0 3.2 8.6 4.0


Documents

The link between extreme precipitation and convective ......has a magnitude of 20% K −1 at the 99th percentile and 149% K 1 at the 99.9th percentile. 3. Convective Organization In